We investigate the role of a single charged impurity on the fractional quantum Hall effect by studying finite systems in spherical, toroidal, and disk geometries. Our qualitative results are independent of the geometry. We study the screening behavior systematically and find that screening charge accumulates at the impurity. The screening charge density shows an interesting oscillation with a characteristic scale of the magnetic length. We also find that the excitation gap is reduced significantly in the presence of the impurity.

We apply a Su-Schriefter-Heeger-like model to study intramolecular electron-phonon interaction for the undoped C60 molecule in which all the translational degrees of freedom for each site are considered. We find that the C60 molecule favors a dimerized ground state and the inclusion of the electron-phonon coupling modifies the phonon spectra such that all the frequencies of the phonon modes shift to red except the A"mode. We also present a semianalytical treatment for the ground-state properties supplemented to the numerical calculations.

There are errors in our derivation of the detailed expressions for the Dzyaloshinskii-Moriya (DM) couplings for the cuprates. The contribution to the DM coupling from the virtual process involving the Cu 3d orbital r -3z should vanish. This becomes transparent when one evaluates the spin-orbit coupling using axes oriented along the tilted Cu-0 octahedra.Consequently, all the terms involving the hopping integral t 2 2 in Ref. 1 should be suppressed. These terms appear in Eqs. (10), (13), and (16). As a result, for LazCu04, in the low-temperature orthogonal phase, one of the DM components d, =0, while in the low-temperature tetragonal phase, d4=0.

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